Inclination measurement is used to determine an inclination of a plane with respect to a known reference plane or a reference coordinate. Leveling is an inclination measurement method with the reference plane perpendicular to the earth's gravitational field, i.e., the horizontal plane. Such a quick and accurate method for measuring an inclination of a machine or an instrument is widely used among the low-cost consumers such as carpenters, and in large industries.
Most of the known inventions for inclination measurement are similar to a balance. When the balance is placed at different inclined planes, the angular difference of the equilibrium positions of the balance arm under the gravity is the basis for measurement. It can be further classified as follows: (1) measurement of the position of a gas-liquid interface. The liquid acts as a balance arm, and the gas-liquid interface acts as an indicator. Traditionally, the position of the interface is measured by naked eyes. Either optical reflection from the interface or a capacitance method is adopted in recent inventions. (2) measurement of the relative position of a fixed arm/plate and a mobile arm/plate. The indicator of the mobile arm is parallel to the gravitational field, and the fixed arm is parallel to the outer case of the inclinometer, i.e.. parallel to the plane to be measured. The angle between the arms is measured directly by a mechanical means with linkage mechanism, or indirectly by means of capacitance change or optical path change.
The U.S. patents related to the inclination measurement having the above discussed principles are: Butler U.S. Pat. No. 4,912,662, Franklin U.S. Pat. No. 4,942,668, Scholian U.S. Pat. No. 4,993,162, Davis U.S. Pat. No. 5,170,567, Carlson U.S. Pat. No. 5,237,753, Yaniger U.S. Pat. No. 5,365, 671, and Piske U.S. Pat. No. 5,371,951.
There are three major disadvantages in the conventional methods. First, the measuring range of the inclination is usually limited to .+-.45.degree., because the measuring arm is usually supported in the middle as a balance. Theoretically, the arm at a .+-.45.degree. position is a metastable point. Thus, an accurate measurement near .+-.45.degree. is difficult. Although by using an additional set of sensing unit parallel to the gravitational field, i.e., perpendicular to the original arm for measuring a higher angle can solve this problem partly, the inclinometer is either less accurate in measurement or complicated in structure. It is also difficult for overhead measurement. Second, fluid is used either directly as an arm, for increasing the differences in dielectric constant for capacitance measurement, or for increasing the differences in reflection index when measuring the optical path. The conventional methods limit the inclinometer to be used in a certain environment, and the inclinometer is not suitable to use at a high (low) temperature, at an overhead position or in vacuum. Third, only the inclined angle along one axis which is usually the balance arm can be obtained by each measurement. The so-called multiaxial measurement cannot be performed directly.
It should be indicated that a piezoelectric resonator to transform and magnify the input signal via electromechanical coupling between the input end and the output end is disclosed in the patents, for example, U.S. Pat. No. 3,736,446. But the reference does not teach to use a piezoelectric resonator as an inclinometer to measure an inclined angle by measuring the vibrating amplitude as disclosed in the present invention.
The use of piezoelectric actuators for changing the angular position of a tilting mirror of a light deflection apparatus has been described in U.S. Pat. No. 4,660,941. But the angular position of the mirror plane in the reference is measured by a capacitance method, which is different from the present invention.
In U.S. Pat. No. 4,843,887, a piezoelectric sensor is used as a strain gauge. A signal induced by the piezoelectric sensor under an applied stress is transformed into a strain value. The present invention uses the induced signal of a piezoelectric body under applied gravitational force to obtain a plane inclination. Accordingly, it is different from the reference.